Post on 14-May-2023
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1. INTRODUCTION In the scope of the Research Project, which is a 5th year course of Chemical
Engineering, it was suggested to research and study the project of software of Heat
Exchangers Design in the base of Visual Basic Application (VBA). Thus, this study although
having an academic origin, its operation have designed to be mostly possible way of situations.
The process of heat exchange between two fluids that are at different temperatures and
separated by a solid wall occurs in many engineering applications. The device that is being
used for this heat exchange is termed as heat exchanger. They are typically classified
according to their flow arrangement and type of construction. The simplest heat exchanger is
one for which the hot and cold fluids move in the same or opposite directions in a concentric
tube construction.
Figure 1 - Operating principle of a parallel-flow concentric tube heat exchanger.
As you see in the parallel flow (co-current) arrangement, the hot and cold fluids enter
at the same end, flow in the same direction, and leave at the same end. In contrast, in the
counter flow arrangement, the fluids enter at the opposite ends, flow in opposite directions,
and leave at opposite ends.
Another common configuration is the shell and tube heat exchanger. It can have some
specific forms according to the number of shell and tube passes and the simplest form, which
involves single tube and shell passes.
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Figure 2- Shell and tube heat exchanger with one shell pass and one tube pass (Cross-
parallel-flow mode of operation).
In my research project there will be two different types of heat exchangers, which are
concentric tube, and shell & tube heat exchangers. Both types were studied according to
different flow arrangements in different problems. The problems will be given and the
unknowns will be solved in VBA program in excel sheet. Until here, there was not any phase
change but, it is also considered due to condensation by introducing in another problem.
Below, different cases will be studied in different heat exchangers with the consequent results.
At the end of the report, you can see the codes of the problems that were performed in Visual
basic application under the title of “Modules.”
mtube
mshell
mpentane
mwater
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2. CONCENTRIC TUBE HEAT EXCHANGERS In this case, we have a concentric tube heat exchanger, which contains an inner and an
annulus part that enables the fluid to flow in the surrounding of the exchanger. It can also be
considered as 1-1 type shell and tube heat exchanger. Actually, the types with more tubes
were considerable but they are mechanically and dynamically less effective comparing to the
shell and tube type. Concentric type has also a shape of hollow cylinder from the cross
sectional view.
2.1 Case 1: Concentric Tube Heat Exchanger with constant Heat Transfer
Coefficients and without Phase Change
Equations that are used in the concentric tube heat exchanger calculation are given as follows:
-Heat rate equation;
Q m Cp T [1]
-LMTD calculation;
)()(
ln
)()(
,,
,,
,,,,ln
inletannulusoutlettube
outletannulusinlettube
inletannulusoutlettubeoutletannulusinlettube
TTTT
TTTTT
For counter-current flow type [2]
)()(
ln
)()(
,,
,,
,,,,ln
outletannulusoutlettube
inletannulusinlettube
outletannulusoutlettubeinletannulusinlettube
TTTT
TTTTT
For co-current flow type [3]
-Overall heat transfer coefficient; 1 1 1( )tubein tubeanU h h [4]
-Design equation;
lnexchangerQ U A T [5]
exchanger out tubeA D L [6]
-NTU method, which is very useful in case of the two outlet temperatures are unknown;
water
oil Di Do
4
min( )exchanger
imum
U ANTU
m Cp
For both flow type [7]
min( ) imumm Cp indicates the minimum value of one of the fluid. [8]
-Thermal efficiency (ε);
1 exp (1
1 exp (1 )
NTU C
C NTU C
Counter-current flow type [9]
1 exp (11NTU CC
Co-current flow type [10]
min
max
CCC
[11]
min min
max max
( )( )
imum
imum
C m CpC m Cp
[12]
, ,
, ,
tube inlet tube outlet
tube inlet annulus inlet
T TT T
[13]
Here you see an illustrative example, which is governed by the given equations above.
Example 2.1
In a concentric tube heat exchanger, which is isolated thermally from the exterior, has a
duty to cool hot oil by using cooling water. The hot oil enters the system into the fine metallic
tube of 25mm diameter at a mass flow rate of 0.6 kg/s. The cooling water enters the
exchanger counter-currently into the annulus section the external diameter of 42mm at the
same mass flow rate. The inlet and outlet temperatures of hot oil are 420 K and 380 K,
respectively. The convective heat transfer coefficients of the oil and water are 847.61 and
3367.22 W/m2K, and the specific heats are 2508 and 4180J/kgK, respectively.
a) Determine the length that the tube should have if the water enters at 290 K?
b) Using the length of the tube (calculated in a) and admitting the water inlet temperature
as 290 K, determine the outlet temperatures of both fluid if the system operates in co-
current?
Solution:
Known: Fluid flow rates, inlet temperatures, and convective heat transfer coefficients for a
counter flow, concentric tube heat exchangers of prescribed inner and outer diameter.
Find: a) Tube length to achieve a desired cold fluid outlet temperature.
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b) Both outlet temperatures of the fluids using the length calculated in a.
Counter-current temperature profile Assumptions:
1) Heat loss to the surroundings is negligible. 2) Thermodynamic properties are constant. 3) Tube wall thermal resistance and fouling factors are negligible.
Part a): Counter-current flow First of all heat released from oil is calculated from the heat rate equation:
oil oilQ m Cp T Secondly, outlet water temperature was calculated via heat rate equation of cooling water by equating to oil heat rate ( oil waterQ Q ):
, ,water out water inwater
QT Tm Cp
Then, lnT is calculated:
)()(
ln
)()(
,,
,,
,,,,ln
inletannulusoutlettube
outletannulusinlettube
inletannulusoutlettubeoutletannulusinlettube
TTTT
TTTTT
1 1 1( )tubein tubeanU h h
lnexchangerQ U A T
lnexchanger
exchanger out tube
exchangertube
out
QAU T
A D LA
LD
x
T (x)
Ttube, inlet
Ttube, outlet
Tannulus, outlet Tannulus, inlet
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Co-current flow Co-current temperature profile
oil oilQ m Cp T
)()(
ln
)()(
,,
,,
,,,,ln
outletannulusoutlettube
inletannulusinlettube
outletannulusoutlettubeinletannulusinlettube
TTTT
TTTTT
1 1 1( )tubein tubeanU h h
lnexchanger
exchanger out tube
exchangertube
out
QAU T
A D LA
LD
Results:
Concentric Tubes Heat Exchanger Type cocurrent
Variables inner (oil) annular(water) m [kg/s] 0,6 0,6
Cp [J/(kg K)] 2508 4180
Tin [K] 420 290
Tout [K] 380 314 Diameter [m] 0,025 0,042
h [J/(K m2 s)] 847,61 3367,22
U [J/(K m2 s)] 677,15
A [m2] 0.94
Ltube [m] 7.14
Duty [J/s] 60192
Concentric Tubes Heat Exchanger Type countercurrent
Variables inner (oil) annular(water) m [kg/s] 0,6 0,6
Cp [J/(kg K)] 2508 4180
Tin [K] 420 290
Tout [K] 380 314 Diameter [m] 0,025 0,042
h [J/(K m2 s)] 847,61 3367,22
U [J/(K m2 s)] 677,15
A [m2] 0,91
Ltube [m] 6.9
Duty [J/s] 60192
x
T (x)
Ttube, inlet
Ttube, outlet
Tannulus, inlet
Tannulus, outlet
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Part b): Counter-current flow Since both outlet temperatures are unknown in this part NTU method will be applied as follows:
min( )exchanger
imum
U ANTU
m Cp
exchanger outA D L
min
min
( )( )
imum oil
imum water
m Cpm Cp
Yields the minimum value
min
max
CCC
1 exp (1
1 exp (1 )
NTU C
C NTU C
Counter-current flow expression
, ,
, ,
tube inlet tube outlet
tube inlet annulus inlet
T TT T
oil oilQ m Cp T
Co-current flow:
min( )exchanger
imum
U ANTU
m Cp
min
max
CCC
1 exp (1
1NTU CC
Co-current flow expression
, ,
, ,
tube inlet tube outlet
tube inlet annulus inlet
T TT T
oil oilQ m Cp T
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Results:
Concentric Tubes Heat Exchanger Type cocurrent
Variables inner (oil) annular (water) m [kg/s] 0,6 0,6
Cp [J/(kg K)] 2508 4180
Tin [K] 420 290
Tout [K] 380 314 Diameter [m] 0,025 0,042
h [J/(K m2 s)] 847,61 3367,22
U [J/(K m2 s)] 677,15
A [m2] 0,94
Ltube [m] 7,14
Duty [J/s] 60218,5
Ntu 0,42
Eps 0,31
Cx 0,6
2.2 Case 2: Concentric Tube Heat Exchanger with Phase Change
In this case, we have steam condensation flows through the annulus part of the
exchanger. Schematically representation of the exchanger is given below.
The equations that are going to be used in the calculation are as follows:
For tube section
Laminar Regime
-Reynolds Number:
20004
Re
wateri
waterwater D
m
[14]
-Nusselt Number: Sieder and Tate Correlation:
Concentric Tubes Heat Exchanger Type countercurrent
Variables inner (oil) annular (water) m [kg/s] 0,6 0,6
Cp [J/(kg K)] 2508 4180
Tin [K] 420 290
Tout [K] 379,95 314 Diameter [m] 0,025 0,042
h [J/(K m2 s)] 847,61 3367,22
U [J/(K m2 s)] 677,15
A [m2] 0,91
Ltube [m] 6,90
Duty [J/s] 60260,3
Ntu 0,41
Eps 0,31
Cx 0,6
Steam
Water Di Do
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14.03/13/13/1 PrRe86.1
stube
iwaterwater L
DNu [15]
Transition Regime -Reynolds Number:
100004
Re2000
wateri
waterwater D
m
[16]
-Nusselt Number:
14.03/23/13/2 1Pr)125(Re116.0
stube
iwaterwater L
DNu
[17]
Turbulent Regime -Reynolds Number:
100004
Re
wateri
waterwater D
m
[18]
-Nusselt Number: The Dittus-Boelter Correlation:
nwaterwaterNu PrRe023.0 8.0 [19]
Where n=0.4 for heating
n=0.3 for cooling
- Heat transfer coefficient
fluidi
i
Nu kh
D
[20]
For annular section
Laminar Regime
-Reynolds Number
2Re 1800steamsteam
steam tube
mL
[21]
10
-Heat Transfer Coefficient
[22]
-Surface Temperature
, ,
22
tube inlet tube outletsat
surface
T TT
T
[23]
Turbulent Regime
-Reynolds Number
2Re 1800steamsteam
steam tube
mL
[24]
-Heat Transfer Coefficient 1/ 41/3 1/ 22 3
,2
20.023 p L LsteamL Lo
L L tube L
Cmg khL k
[25]
These equations are illustrated with an example problem below.
Example 2.2
A thin walled concentric tube heat exchanger of 15m length is to be used to heat
deionised water, which enters to the system at 40oC at a flow rate of 1.5 kg/s, flows through
the inner tube of 30mm diameter. In contrast saturated steam is supplied at 1atm (100oC) to
the annulus section formed with the outer tube of 60mm diameter. Determine the outlet
temperature of deionised water (Twater,out) and mass flow rate of condensation (mcondensation)?
Thermo physical properties of water @ 50 oC :
Density, [kg/m3] 982.3
Heat capacity, [J/kgK] 4181
Viscosity, [kg/ms] 548x10-6
Prandtl number, [-] 3.56
Thermal conductivity, [W/mK] 0.643
4/13
)()(729.0
osurfacesatL
LvLLo DTT
kgh
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Thermo physical properties of saturated steam @ 100 oC and 1 atm:
Liquid density, [kg/m3] 957.8
Vapour density, [kg/m3] 0.6
Heat capacity, [J/kgK] 4217
Heat of condensation, [J/kg] 2257000
Viscosity, [kg/ms] 280x10-6
Prandtl number, [-] 1.76
Thermal conductivity, [W/mK] 0.68
Solution:
Known: Water flow rate, inlet temperatures, thermo physical properties of both fluid, and
dimensional properties of the system.
Find: Outlet temperature of deionised water, mass flow rate of condensed steam, heat transfer
coefficients for inner and annulus section, and duties by heat rate and by design equation.
In the system, two heat duties (Q1 and Q2) are defined to be determined from different
ways. By doing that, we will be able to check the results in the iterative procedure.
1 water waterQ m Cp T
Twater,outlet = ? Assumption: Twater,outlet=Ttube,outlet=360 K Then Q1 is obtained. Since; Q1 = Q2
2steam
Qm
is determined.
Then, to satisfy the assumed temperature is right, the difference between Q1 and Q2 is expected to be zero,
1 2Q Q Q Then other parameters are obtained as follows:
1 1 1( )i oU h h
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For hi:
20004
Re
wateri
waterwater D
m
Laminar Regime
Sieder and Tate Correlation:
14.03/13/13/1 PrRe86.1
stube
iwaterwater L
DNu
100004
Re2000
wateri
waterwater D
m
Transition Regime
14.03/2
3/13/2 1Pr)125(Re116.0
stube
iwaterwater L
DNu
100004
Re
wateri
waterwater D
m
Turbulent Regime
The Dittus-Boelter Correlation:
nwaterwaterNu PrRe023.0 8.0
Where n=0.4 for heating
n=0.3 for cooling
Then;
For ho:
2Re 1800steamsteam
steam tube
mL
Laminar Regime
, ,
22
tube inlet tube outletsat
surface
T TT
T
i
wateri D
kNuh
4/13
)()(729.0
osurfacesatL
LvLLo DTT
kgh
13
2Re 1800steamsteam
steam tube
mL
Turbulent Regime
1/ 41/3 1/ 22 3
,2
20.023 p L LsteamL Lo
L L tube L
Cmg khL k
And finally;
1 1 1( )i oU h h is obtained.
)()(
ln
)()(
,,
,,
,,,,ln
inlettubeoutletannulus
outlettubeinletannulus
inlettubeoutletannulusoutlettubeinletannulus
TTTT
TTTTT
exchanger o tubeA D L
lnexchanger
QUA T
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Results:
Concentric Tubes Heat Exchanger
Type countercurrent
Variables inner (water) annular (steam)
m [kg/s] 1,5 0,13
[J/kg] 2257000
Cp [J/(kg K)] 4180 4217
ρ [kg/m3] 982,3 957,8 0,6
μ[kg/m.s] 0,00055 0,00028
prandtl [-] 3,56 1,76
reynolds [-] 77447,66 62,13
nusselt [-] 311,54
kfluid [W/m.k] 0,643 0,68
d [m] 0,045 0,09
h [W/m2.K] 4451,57 7914,04
Tin [K] 313,00 373,00
Tout [K] 359,80 373,00
dhydraulic [m] 0,045
ktube [W/m.k] 80,2
ltube [m] 15
areaexchanger[m2] 4,24
ΔTln [K] 30,91
uexchanger [W/m2.K] 2849,02
uexchanger [W/m2.K] 2237,98
dutyexchanger [W] 293410,00
dutyexchanger [W] 293410,00
Tsat [K] 373
Tsurface [K] 354,70
gravity [m/s2] 9,81
Difference 0,00
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3. SHELL AND TUBE HEAT EXCHANGERS Shell and tube heat exchangers are commonly used as oil coolers, power condensers,
preheaters and steam generators in both fossil fuel and nuclear-based energy production
applications. They are also widely used in process applications and in the air conditioning and
refrigeration industry. Although they are not specially compact, their robustness, and shape
make them well suited for high pressure operations. In view of the diverse engineering
applications and basic configuration of shell and tube heat exchangers, the thermal analysis
and design of such exchangers form an integral part of the undergraduate mechanical and
chemical engineering curricula of most universities.
3.1 Case: Shell and Tube Heat Exchanger without Phase Change
In this case, shell and tube heat exchanger rate will be studied in case of a deposit formation
inside of the tubes due to the flowing fluid without any phase change. Besides, fouling factor
(Rfi) is also going to be studied.
Here are the equations used in this application;
-Heat rate:
Q m and Q m Cp T [25]
-Design Equation:
lnexchangerQ U A F T [26]
-Overall heat exchange coefficient:
mshell
mtube
mshell
mtube
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1( )total exchangerU R A [27]
-Total resistance inside the tubes:
ln
1 1total
i i tube o o
xRh A k A h A
[28]
-Fouling factor:
intint ln tan
1 1fi total erior
water erior tube pen e exterior
xR R Ah A k A h A
[29]
-Logarithmic area:
intln
int
lnexterior erior
exterior
erior
A AA AA
[30]
-Internal and external area:
int erior in tube tubeA D L N [31]
exterior out tube tubeA D L N [32]
Below, you can see an illustrative example related to the equations above.
Example 3.1
A shell and tube heat exchanger, which possesses 140 steel tubes of 2m length, 19mm of
external and 16mm of internal diameter, isolated thermally from the exterior. The thermal
conductivity of the steel tube is 53,4W/mK. It is intended to use to condense 2.8 kg/s of
saturated pentane at 2atm in the shell side. The saturation temperature of the pentane is 60oC
and the latent heat of condensation is 313500 J/kg. In contrast, cooling water, enters at 15oC ,
circulates inside the tubes. The convective heat transfer coefficients are given by the
following expressions:
For water hwater =290 x (mwater )0.8
For pentane hpentane=1861.7 x (mpentane) 0.25
mwater and mpentane are the mass flow rates of water and pentane in kg/s; hwater and hpentane are in
W/m2K.
a) Determine the flow rate of water necessary to condense 2.8 kg/s of pentane?
b) Due to the formation of deposits inside the tubes, the flow rate of pentane was
decreased to 1.9 kg/s. Assuming that the flow rate of water is 20.83 kg/s,
determine the thermal resistance of the formed deposits?
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Solution: Known: Flow rate of shell side fluid, inlet temperatures, and convective heat transfer
coefficients as functions of mass flow rates, dimensions of shell and tube heat exchanger.
Find: Required water mass flow rate to condense pentane.
Thermal resistance of the formed deposits.
Schematic:
Part a):
Heat released by pentane:
tanpen eQ m
Trial-error procedure is required due to not to know the outlet temperatures of water and mass
flow rate.
Assuming Twater,out=300 K
waterwater
QmCp T
0.8 2290 (17.5) 2864.27 /waterh watt m K
The procedure will continue until the difference between heat of condensation and design
equation becomes zero. Otherwise new assumption is required.
lnexchangerQ U A T
1( )total exchangerU R A
int ln tan
1 1total
water erior tube pen e exterior
xRh A k A h A
mpentane
mwater
mpentane
mwater
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exchanger exteriorA A
int erior in tube tubeA D L N
exterior out tube tubeA D L N
intln
int
lnexterior erior
exterior
erior
A AA AA
design condensationDifference Q Q Q
Results:
Shell & Tube Heat Exchanger
Type 1-shell pass Variables tube side (water) shell side (pentane) m [kg/s] 17,50 2,80
Cp [J/(kg K)], [J/kg] 4180 313500
Tin [K] 288 333
Tout [K] 300,00 333
h [J/(K m2 s)] 2864,27 2408
U [J/(K m2 s)] 1122,39
Din [m] 0,016
Dout [m] 0,019
Atubein [m2] 17,02
Atubeout [m2] 20,21
Aln [m2] 18,57
Ntube [-] 140
Ltube [m] 2,42
x [m] 0,003
ktube [J/s m K] 53,41
Tln [K] 38,69
Rtotal [K s/J] 0,0000441
F [-] 1
Duty [J/s] 877800,00
Design Duty [J/s] 877800,00
Difference 0
Part b):
tanpen eQ m
, ,tube outlet tube inletwater
QT Tm Cp
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)()(
ln
)()(
,,
,,
,,,,ln
inletshelloutlettube
outletshellinlettube
inletshelloutlettubeoutletshellinlettube
TTTT
TTTTT
exchanger out tubeA D L N
lnexchanger
QUA T
1( )total exchangerR U A
intint ln tan
1 1fi total erior
water erior tube pen e exterior
xR R Ah A k A h A
Results:
Shell & Tube Heat Exchanger
Type 1-shell pass Variables tube side(water) shell side(pentane) m [kg/s] 20,83 1,90
Cp [J/(kg K)], [J/kg] 4180 313500
Tin [K] 288 333
Tout [K] 294,84 333
h [J/(K m2 s)] 3292,57 2186
U [J/(K m2 s)] 859,08
Din [m] 0,016
Dout [m] 0,019
Atubein [m2] 14,07
Atubeout [m2] 16,71
Aln [m2] 15,36
Ntube [-] 140
Ltube [m] 2
x [m] 0,003
ktube [J/s m K] 53,41
Tln [K] 41,49
Rtotal [K/W] 0,00007
Rfi [m2 K/W] 0,0004
F [-] 1
Duty [J/s] 595650,00
Duty [J/s] 595650,00
20
4. NOMENCLATURE Aexchanger: Exchanger Area [m2]
Ainterior: Internal area [m2]
Aexterior: External area [m2]
Aln: Logarithmic area [m2]
Q: Heat transfer rate [W]
U: Overall heat transfer coefficient [W/m2.K]
hi: Inside heat transfer coefficient [W/m2.K]
ho: Outside/exterior heat transfer coefficient [W/m2.K]
Re: Reynolds number [-]
Resteam: Reynolds number for the condensed steam [-]
Rewater: Reynolds number for the water [-]
Nu: Nusselt number [-]
Pr: Prandtl number [-]
PrL: Prandtl number for the liquid [-]
Prwater: Prandtl number for the water [-]
Di: Internal diameter [m]
Do: External diameter [m]
Dh: Hydraulic diameter [m]
V: Velocity of the fluid [m/s]
g: Gravitational acceleration [m/s2]
ktube: Thermal conductivity of the tube [W/m.K]
msteam: Mass flow rate of condensate [kg/s]
L : Viscosity of condensate [kg/m.s]
s : Viscosity at the surface temperature [kg/m.s]
L: Length of the tube [m]
mwater: Mass flow rate of water [kg/s]
moil: Mass flow rate of oil [kg/s]
Cp,L: heat capacity of condensate evaluated at film temperature [J/kg.K]
kL: Thermal conductivity of the condensate [W/m.K]
: Latent heat of condensation [J/kg]
L : Density of the condensate [kg/m3]
v : Density of the vapour [kg/m3]
21
Vv: Velocity of the vapour in the tube [m/s]
v : Viscosity of the vapour in the tube [kg/m.s]
Tsat: Saturation temperature of the vapour [K]
Tsurface: Surface temperature of the tube [K]
Tm: Mean temperature [K]
Ts,o: Outlet surface temperature of the tube [K]
N: Number of the tubes [-]
Rtotal: Total resistance [K/W]
Rfi: Fouling factor [m2K/W]
NTU: Number of transfer units [-]
ε : Thermal Efficiency [-]
22
5. REFERENCES [1] P., Incropera, Frank, P., De Witt, David, Introduction to heat transfer, 4th edition, John
Wiley & Sons.
[2] The heat transfer notes from Prof. Luis Melo.
[3] Heat Exchangers, Selection Rating & Design, Sadik Kakac & Hongtan Liu, CRC Press,
2nd Edition, 2002
[4] Shell & Tube Heat Exchanger Design Software for Educational Applications. Int. J.
Engng. Ed. Vol. 14, No. 3, p 217-224, 1998 K.C. Leong, K.C. Toh, Y.C. Leong
[5] Wolverine Tube Heat Transfer Data Book, www.wolverine.com.
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6. MODULES Here are the modules of the illustrated problems, which were programmed in VBA.
Example 2.1: Have two parts; Part_A and Part_B and meanwhile both parts have two
different stream types; co-current and counter-current flow.
Part_A:
Sub main_Part_A_cocurrent()
Declaration of variables
Dim name_sheet As String
Dim m_tubein As Double Dim m_tubean As Double Dim cp_tubein As Double Dim cp_tubean As Double Dim h_tubein As Double Dim h_tubean As Double Dim d_tubein As Double Dim d_tubean As Double Dim tin_tubein As Double Dim tout_tubein As Double Dim tin_tubean As Double Dim tout_tubean As Double Dim u_exchanger As Double Dim l_exchanger As Double Dim duty_exchanger As Double Dim delt_ln As Double Dim area_exchanger As Double Dim l_tube As Double Inputs name_sheet = "Part_A" m_tubein = Sheets(name_sheet).Cells(4, 3).Value m_tubean = Sheets(name_sheet).Cells(4, 4).Value cp_tubein = Sheets(name_sheet).Cells(5, 3).Value cp_tubean = Sheets(name_sheet).Cells(5, 4).Value tin_tubein = Sheets(name_sheet).Cells(6, 3).Value tout_tubein = Sheets(name_sheet).Cells(7, 3).Value tin_tubean = Sheets(name_sheet).Cells(6, 4).Value d_tubein = Sheets(name_sheet).Cells(8, 3).Value d_tubean = Sheets(name_sheet).Cells(8, 4).Value h_tubein = Sheets(name_sheet).Cells(9, 3).Value h_tubean = Sheets(name_sheet).Cells(9, 4).Value If IsEmpty(Sheets(name_sheet).Cells(6, 3).Value) = True Then tin_tubean = Sheets(name_sheet).Cells(6, 4).Value tout_tubein = Sheets(name_sheet).Cells(7, 3).Value
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tout_tubean = Sheets(name_sheet).Cells(7, 4).Value duty_exchanger = m_tubean * cp_tubean * (tout_tubean - tin_tubean) tin_tubein = tout_tubein + duty_exchanger / (m_tubein * cp_tubein) Sheets(name_sheet).Cells(6, 3).Value = tin_tubein ElseIf IsEmpty(Sheets(name_sheet).Cells(6, 4)) = True Then tin_tubein = Sheets(name_sheet).Cells(6, 3).Value tout_tubein = Sheets(name_sheet).Cells(7, 3).Value tout_tubean = Sheets(name_sheet).Cells(7, 4).Value duty_exchanger = m_tubein * cp_tubein * (tin_tubein - tout_tubein) tin_tubean = tout_tubean - duty_exchanger / (m_tubean * cp_tubean) Sheets(name_sheet).Cells(6, 4) = tin_tubean ElseIf IsEmpty(Sheets(name_sheet).Cells(7, 4)) = True Then tin_tubein = Sheets(name_sheet).Cells(6, 3).Value tout_tubein = Sheets(name_sheet).Cells(7, 3).Value tin_tubean = Sheets(name_sheet).Cells(6, 4).Value duty_exchanger = m_tubein * cp_tubein * (tin_tubein - tout_tubein) tout_tubean = tin_tubean + duty_exchanger / (m_tubean * cp_tubean) Sheets(name_sheet).Cells(7, 4) = tout_tubean Else tin_tubein = Sheets(name_sheet).Cells(6, 3).Value tin_tubean = Sheets(name_sheet).Cells(6, 4).Value tout_tubean = Sheets(name_sheet).Cells(7, 4).Value duty_exchanger = m_tubean * cp_tubean * (tout_tubean - tin_tubean) tout_tubein = tin_tubein - duty_exchanger / (m_tubein * cp_tubein) Sheets(name_sheet).Cells(7, 3).Value = tout_tubein
End If
Calculations
u_exchanger = 1 / ((1 / h_tubein) + (1 / h_tubean))
delt_ln = ((tin_tubein - tin_tubean) - (tout_tubein - tout_tubean) / Log((tin_tubein -
tin_tubean) / (tout_tubein - tout_tubean)))
area_exchanger = duty_exchanger / (u_exchanger * delt_ln)
l_tube = area_exchanger / (d_tubein * Application.WorksheetFunction.Pi())
Print Results
Sheets(name_sheet).Cells(7, 4).Value = tout_tubean
Sheets(name_sheet).Cells(7, 4).Font.ColorIndex = 3
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Sheets(name_sheet).Cells(7, 4).Font.Bold = True
Sheets(name_sheet).Cells(10, 3).Value = Round(u_exchanger, 2)
Sheets(name_sheet).Cells(10, 3).Font.ColorIndex = 3
Sheets(name_sheet).Cells(10, 3).Font.Bold = True
Sheets(name_sheet).Cells(11, 3).Value = Round(area_exchanger, 2)
Sheets(name_sheet).Cells(11, 3).Font.ColorIndex = 3
Sheets(name_sheet).Cells(11, 3).Font.Bold = True
Sheets(name_sheet).Cells(12, 3).Value = Round(l_tube, 2)
Sheets(name_sheet).Cells(12, 3).Font.ColorIndex = 3
Sheets(name_sheet).Cells(12, 3).Font.Bold = True
Sheets(name_sheet).Cells(13, 3).Value = duty_exchanger
Sheets(name_sheet).Cells(13, 3).Font.ColorIndex = 3
Sheets(name_sheet).Cells(13, 3).Font.Bold = True
End Sub
Sub main_Part_A_countercurrent()
Declaration of variables
Dim name_sheet As String
Dim m_tubein As Double Dim m_tubean As Double Dim cp_tubein As Double Dim cp_tubean As Double Dim h_tubein As Double Dim h_tubean As Double Dim d_tubein As Double Dim d_tubean As Double Dim tin_tubein As Double Dim tout_tubein As Double Dim tin_tubean As Double Dim tout_tubean As Double
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Dim u_exchanger As Double Dim l_exchanger As Double Dim duty_exchanger As Double Dim delt_ln As Double Dim area_exchanger As Double Dim l_tube As Double Inputs name_sheet = "Part_A" m_tubein = Sheets(name_sheet).Cells(4, 3).Value m_tubean = Sheets(name_sheet).Cells(4, 4).Value cp_tubein = Sheets(name_sheet).Cells(5, 3).Value cp_tubean = Sheets(name_sheet).Cells(5, 4).Value tin_tubein = Sheets(name_sheet).Cells(6, 3).Value tout_tubein = Sheets(name_sheet).Cells(7, 3).Value tin_tubean = Sheets(name_sheet).Cells(6, 4).Value d_tubein = Sheets(name_sheet).Cells(8, 3).Value d_tubean = Sheets(name_sheet).Cells(8, 4).Value h_tubein = Sheets(name_sheet).Cells(9, 3).Value h_tubean = Sheets(name_sheet).Cells(9, 4).Value If IsEmpty(Sheets(name_sheet).Cells(6, 3).Value) = True Then tin_tubean = Sheets(name_sheet).Cells(6, 4).Value tout_tubein = Sheets(name_sheet).Cells(7, 3).Value tout_tubean = Sheets(name_sheet).Cells(7, 4).Value duty_exchanger = m_tubean * cp_tubean * (tout_tubean - tin_tubean) tin_tubein = tout_tubein + duty_exchanger / (m_tubein * cp_tubein) Sheets(name_sheet).Cells(6, 3).Value = tin_tubein ElseIf IsEmpty(Sheets(name_sheet).Cells(7, 3).Value) = True Then tout_tubean = Sheets(name_sheet).Cells(7, 4).Value tin_tubein = Sheets(name_sheet).Cells(6, 3).Value tin_tubean = Sheets(name_sheet).Cells(6, 4).Value duty_exchanger = m_tubean * cp_tubean * (tout_tubean - tin_tubean) tout_tubein = tin_tubein - duty_exchanger / (m_tubein * cp_tubein) Sheets(name_sheet).Cells(7, 3).Value = tout_tubein ElseIf IsEmpty(Sheets(name_sheet).Cells(6, 4)) = True Then tin_tubein = Sheets(name_sheet).Cells(6, 3).Value tout_tubean = Sheets(name_sheet).Cells(7, 4).Value tout_tubein = Sheets(name_sheet).Cells(7, 3).Value duty_exchanger = m_tubein * cp_tubein * (tin_tubein - tout_tubein) tin_tubean = tout_tubean - duty_exchanger / (m_tubean * cp_tubean) Sheets(name_sheet).Cells(6, 4).Value = tin_tubean Else
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tin_tubein = Sheets(name_sheet).Cells(6, 3).Value tout_tubein = Sheets(name_sheet).Cells(7, 3).Value tin_tubean = Sheets(name_sheet).Cells(6, 4).Value duty_exchanger = m_tubein * cp_tubein * (tin_tubein - tout_tubein) tout_tubean = tin_tubean + duty_exchanger / (m_tubean * cp_tubean) Sheets(name_sheet).Cells(7, 4).Value = tout_tubean End If
Calculations
u_exchanger = 1 / (1 / h_tubein + 1 / h_tubean)
delt_ln = ((tin_tubein - tout_tubean) - (tout_tubein - tin_tubean)) / _
Log((tin_tubein - tout_tubean) / (tout_tubein - tin_tubean))
area_exchanger = duty_exchanger / (u_exchanger * delt_ln)
l_tube = area_exchanger / (d_tubein * Application.WorksheetFunction.Pi())
Print results
Sheets(name_sheet).Cells(7, 4).Value = tout_tubean
Sheets(name_sheet).Cells(7, 4).Font.ColorIndex = 5
Sheets(name_sheet).Cells(7, 4).Font.Bold = True
Sheets(name_sheet).Cells(10, 3).Value = Round(u_exchanger, 2)
Sheets(name_sheet).Cells(10, 3).Font.ColorIndex = 5
Sheets(name_sheet).Cells(10, 3).Font.Bold = True
Sheets(name_sheet).Cells(11, 3).Value = Round(area_exchanger, 2)
Sheets(name_sheet).Cells(11, 3).Font.ColorIndex = 5
Sheets(name_sheet).Cells(11, 3).Font.Bold = True
Sheets(name_sheet).Cells(12, 3).Value = Round(l_tube, 1)
Sheets(name_sheet).Cells(12, 3).Font.ColorIndex = 5
Sheets(name_sheet).Cells(12, 3).Font.Bold = True
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Sheets(name_sheet).Cells(13, 3).Value = duty_exchanger
Sheets(name_sheet).Cells(13, 3).Font.ColorIndex = 5
Sheets(name_sheet).Cells(13, 3).Font.Bold = True
End Sub
Example 2.2: In the problem, we have a concentric tube heat exchanger. The objective is to heat the
deionised water by condensing the saturated steam. The heat transfer coefficients are going to
be determined but before mass flow rate of steam and water outlet temperature are to be found.
The “Goal Seek” method is applied for the calculation procedure.
Range("c29").GoalSeek Goal:=0, ChangingCell:=Range("c16")
Example 3.1:
Part_A: In the first part of this problem, there is a trial-error procedure. In normal case,
problem could be solved by using several numerical methods such as “Newton-Raphson,
Bisection” methods etc. But for simplicity, it was solved by using “Goal Seek” method. This
method was applied to the problem as follows:
Firstly, water outlet temperature is assumed with an arbitrary value between water inlet and
saturated pentane inlet temperature. Heat duty of the exchanger has already calculated by the
mass flow rate of sat’d pentane and heat of condensation. Then, mass flow rate of water is
calculated by the heat rate equation. Finally, the procedure is let to proceed until the
difference between the heat duties becomes zero.
Part_A:
Sub main_Part_A()
Declaration of variables
' Dim name_sheet As String
' Dim m_tube As Double ' Dim m_shell As Double ' Dim cp_tube As Double ' Dim cp_shell As Double ' Dim h_tube As Double
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' Dim h_shell As Double ' Dim d_tubein As Double ' Dim d_tubeout As Double ' Dim tin_tube As Double ' Dim tout_tube As Double ' Dim tin_shell As Double ' Dim tout_shell As Double ' ' Dim u_exchanger As Double ' Dim R_total As Double ' Dim area_tubein As Double ' Dim area_tubeout As Double ' Dim area_ln As Double ' Dim del_x As Double ' Dim l_exchanger As Double ' Dim duty_exchanger As Double ' Dim delt_ln As Double ' Dim area_exchanger As Double ' Dim l_tube As Double ' Dim N_tube As Double ' Dim k_tube As Double ' Dim f_correction As Double Inputs ' name_sheet = "Part_A"' 'm_tube = Sheets(name_sheet).Cells(4, 3).Value 'm_shell = Sheets(name_sheet).Cells(4, 4).Value 'cp_tube = Sheets(name_sheet).Cells(5, 3).Value 'cp_shell = Sheets(name_sheet).Cells(5, 4).Value 'tin_tube = Sheets(name_sheet).Cells(6, 3).Value 'tin_shell = Sheets(name_sheet).Cells(6, 4).Value 'tout_shell = Sheets(name_sheet).Cells(7, 4).Value 'h_tube = Sheets(name_sheet).Cells(8, 3).Value 'h_shell = Sheets(name_sheet).Cells(8, 4).Value 'u_exchanger = Sheets(name_sheet).Cells(9, 3).Value 'd_tubein = Sheets(name_sheet).Cells(10, 3).Value 'd_tubeout = Sheets(name_sheet).Cells(11, 3).Value 'area_tubein = Sheets(name_sheet).Cells(12, 3).Value 'area_tubeout = Sheets(name_sheet).Cells(13, 3).Value 'area_ln = Sheets(name_sheet).Cells(14, 3).Value 'N_tube = Sheets(name_sheet).Cells(15, 3).Value 'l_tube = Sheets(name_sheet).Cells(16, 3).Value 'del_x = Sheets(name_sheet).Cells(17, 3).Value 'k_tube = Sheets(name_sheet).Cells(18, 3).Value 'f_correction = Sheets(name_sheet).Cells(21, 3).Value
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Calculations 'duty_exchanger = m_shell * cp_shell
'area_tubeout = Application.WorksheetFunction.Pi() * d_tubeout * l_tube * N_tube
'area_tubein = Application.WorksheetFunction.Pi() * d_tubein * l_tube * N_tube
'area_ln = (area_tubeout - area_tubein) / Log(area_tubeout / area_tubein)
'h_shell = 207 * m_shell ^ 0.25
'm_tube = duty_exchanger / (cp_tube * (tout_tube - tin_tube))
'h_tube = 0.357 * m_tube ^ 0.8
'u_exchanger = 1 / (R_total * area_tubeout)
'R_total = (1 / (h_tube * area_tubein)) + (del_x / (k_tube * area_ln)) + _
'(1 / (h_shell * area_tubeout))
'delt_ln = ((tin_shell - tout_tube) - (tout_shell - tin_tube)) / _
' Log((tin_shell - tout_tube) / (tout_shell - tin_tube)
Print results
' Sheets(name_sheet).Cells(4, 3).Value = m_tube
' Sheets(name_sheet).Cells(4, 3).Font.ColorIndex = 5
' Sheets(name_sheet).Cells(4, 3).Font.Bold = True
'Sheets(name_sheet).Cells(7, 3).Value = tout_tube
'Sheets(name_sheet).Cells(7, 3).Font.ColorIndex = 5
'Sheets(name_sheet).Cells(7, 3).Font.Bold = True
' Sheets(name_sheet).Cells(8, 3).Value = h_tube
' Sheets(name_sheet).Cells(8, 3).Font.ColorIndex = 5
' Sheets(name_sheet).Cells(8, 3).Font.Bold = True
' Sheets(name_sheet).Cells(9, 3).Value = u_exchanger
' Sheets(name_sheet).Cells(9, 3).Font.ColorIndex = 5
' Sheets(name_sheet).Cells(9, 3).Font.Bold = True
'Sheets(name_sheet).Cells(19, 3).Value = delt_ln
'Sheets(name_sheet).Cells(19, 3).Font.ColorIndex = 5
'Sheets(name_sheet).Cells(19, 3).Font.Bold = True
' Sheets(name_sheet).Cells(20, 3).Value = R_total
' Sheets(name_sheet).Cells(20, 3).Font.ColorIndex = 5
'Sheets(name_sheet).Cells(20, 3).Font.Bold = True
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Range("c24").GoalSeek Goal:=0, ChangingCell:=Range("c16")
End Sub
Part_B: In the second part, it is aimed to obtain the thermal resistance (Rf) inside the tubes of
the formed deposits. These deposits occur due to the some contaminants of the fluid.
Sub main_Part_B() Declaration of variables
Dim name_sheet As String Dim m_tube As Double Dim m_shell As Double Dim cp_tube As Double Dim cp_shell As Double Dim h_tube As Double Dim h_shell As Double Dim d_tubein As Double Dim d_tubeout As Double Dim tin_tube As Double Dim tout_tube As Double Dim tin_shell As Double Dim tout_shell As Double Dim u_exchanger As Double Dim R_total As Double Dim R_fi As Double Dim area_tubein As Double Dim area_tubeout As Double Dim area_ln As Double Dim del_x As Double Dim l_exchanger As Double Dim duty_exchanger As Double Dim delt_ln As Double Dim area_exchanger As Double Dim l_tube As Double Dim N_tube As Double Dim k_tube As Double Dim f_correction As Double
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Inputs name_sheet = "Part_B" m_tube = Sheets(name_sheet).Cells(4, 3).Value m_shell = Sheets(name_sheet).Cells(4, 4).Value cp_tube = Sheets(name_sheet).Cells(5, 3).Value cp_shell = Sheets(name_sheet).Cells(5, 4).Value tin_tube = Sheets(name_sheet).Cells(6, 3).Value tin_shell = Sheets(name_sheet).Cells(6, 4).Value tout_shell = Sheets(name_sheet).Cells(7, 4).Value h_shell = Sheets(name_sheet).Cells(8, 4).Value d_tubein = Sheets(name_sheet).Cells(10, 3).Value d_tubeout = Sheets(name_sheet).Cells(11, 3).Value area_tubein = Sheets(name_sheet).Cells(12, 3).Value area_tubeout = Sheets(name_sheet).Cells(13, 3).Value area_ln = Sheets(name_sheet).Cells(14, 3).Value N_tube = Sheets(name_sheet).Cells(15, 3).Value l_tube = Sheets(name_sheet).Cells(16, 3).Value del_x = Sheets(name_sheet).Cells(17, 3).Value k_tube = Sheets(name_sheet).Cells(18, 3).Value f_correction = Sheets(name_sheet).Cells(22, 3).Value Calculations duty_exchanger = m_shell * cp_shell tout_tube = duty_exchanger / (cp_tube * m_tube) + tin_tube area_tubeout = Application.WorksheetFunction.Pi() * d_tubeout * l_tube * N_tube area_tubein = Application.WorksheetFunction.Pi() * d_tubein * l_tube * N_tube area_ln = (area_tubeout - area_tubein) / Log(area_tubeout / area_tubein) h_shell = 207 * (m_shell * 3600) ^ 0.25 * 4180 / 3600 h_tube = 0.357 * (m_tube * 3600) ^ 0.8 * 4180 / 3600 delt_ln = ((tin_shell - tout_tube) - (tout_shell - tin_tube)) / _ Log((tin_shell - tout_tube) / (tout_shell - tin_tube)) u_exchanger = duty_exchanger / (delt_ln * area_tubeout) R_total = 1 / (u_exchanger * area_tubeout) R_fi = R_total - (1 / (h_tube * area_tubein)) + (del_x / (k_tube * area_ln)) + _ (1 / (h_shell * area_tubeout) * area_tubein)
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Print results Sheets(name_sheet).Cells(7, 3).Value = tout_tube Sheets(name_sheet).Cells(7, 3).Font.ColorIndex = 5 Sheets(name_sheet).Cells(7, 3).Font.Bold = True Sheets(name_sheet).Cells(9, 3).Value = u_exchanger Sheets(name_sheet).Cells(9, 3).Font.ColorIndex = 5 Sheets(name_sheet).Cells(9, 3).Font.Bold = True Sheets(name_sheet).Cells(19, 3).Value = delt_ln Sheets(name_sheet).Cells(19, 3).Font.ColorIndex = 5 Sheets(name_sheet).Cells(19, 3).Font.Bold = True Sheets(name_sheet).Cells(20, 3).Value = Round(R_total, 5) Sheets(name_sheet).Cells(20, 3).Font.ColorIndex = 5 Sheets(name_sheet).Cells(20, 3).Font.Bold = True Sheets(name_sheet).Cells(21, 3).Value = Round(R_fi, 5) Sheets(name_sheet).Cells(21, 3).Font.ColorIndex = 5 Sheets(name_sheet).Cells(21, 3).Font.Bold = True End Sub
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7. CONCLUSION In this research report, I tried to learn how to programme the basic design
applications of heat exchangers based on VBA. During one year period, I was supervised by
Ass. Prof. Fernando Martins. With his useful information about programming, I have gained
different point of view for an engineer in the programming language area. And, Prof. Luis
Melo; with his valuable distributions, we have found our right way in some challenging points.
I would like to thank especially to these two people, for their patience and for their
interests in any situation. I felt myself very lucky to be studied with them.